The Road to Reality: A Complete Guide to the Laws of the Universe

ISBN-13: 9780679776314 / Angielski / Miękka / 2007 / 1136 str.

Roger Penrose

Opis

Roger Penrose, one of the most accomplished scientists of our time, presents the only comprehensive and comprehensible account of the physics of the universe. From the very first attempts by the Greeks to grapple with the complexities of our known world to the latest application of infinity in physics, The Road to Reality carefully explores the movement of the smallest atomic particles and reaches into the vastness of intergalactic space. Here, Penrose examines the mathematical foundations of the physical universe, exposing the underlying beauty of physics and giving us one the most important works in modern science writing.

Recenzje

A comprehensive guide to physics big picture, and to the thoughts of one of the world s most original thinkers. The New York Times

Simply astounding. . . . Gloriously variegated. . . . Pure delight. . . . It is shocking that so much can be explained so well. . . . Penrose gives us something that has been missing from the public discourse on science lately a reason to live, something to look forward to. American Scientist

A remarkable book . . . teeming with delights. Nature

This is his magnum opus, the culmination of an already stellar career and a comprehensive summary of the current state of physics and cosmology. It should be read by anyone entering the field and referenced by everyone working in it. The New York Sun

Extremely comprehensive. . . . The Road to Reality unscores the fact that Penrose is one of the world s most original thinkers. Tucson Citizen

What a joy it is to read a book that doesn't simplify, doesn't dodge the difficult questions, and doesn't always pretend to have answers. . . . Penrose s appetite is heroic, his knowledge encyclopedic, his modesty a reminder that not all physicists claim to be able to explain the world in 250 pages.
The Times (London)

For physics fans, the high point of the year will undoubtedly be The Road to Reality.
The Guardian

A truly remarkable book...Penrose does much to reveal the beauty and subtlety that connects nature and the human imagination, demonstrating that the quest to understand the reality of our physical world, and the extent and limits of our mental capacities, is an awesome, never-ending journey rather than a one-way cul-de-sac. London Sunday Times

Penrose s work is genuinely magnificent, and the most stimulating book I have read in a long time. Scotland on Sunday

Science needs more people like Penrose, willing and able to point out the flaws in fashionable models from a position of authority and to signpost alternative roads to follow. The Independent

Spis treści

Preface
Acknowledgements
Notation
Prologue

1 The roots of science
1.1 The quest for the forces that shape the world
1.2 Mathematical truth
1.3 Is Plato s mathematical world real ?
1.4 Three worlds and three deep mysteries
1.5 The Good, the True, and the Beautiful

2 An ancient theorem and a modern question
2.1 The Pythagorean theorem
2.2 Euclid s postulates
2.3 Similar-areas proof of the Pythagorean theorem
2.4 Hyperbolic geometry: conformal picture
2.5 Other representations of hyperbolic geometry
2.6 Historical aspects of hyperbolic geometry
2.7 Relation to physical space

3 Kinds of number in the physical world
3.1 A Pythagorean catastrophe?
3.2 The real-number system
3.3 Real numbers in the physical world
3.4 Do natural numbers need the physical world?
3.5 Discrete numbers in the physical world

4 Magical complex numbers
4.1 The magic number i
4.2 Solving equations with complex numbers
4.3 Convergence of power series
4.4 Caspar Wessel s complex plane
4.5 How to construct the Mandelbrot set

5 Geometry of logarithms, powers, and roots
5.1 Geometry of complex algebra
5.2 The idea of the complex logarithm
5.3 Multiple valuedness, natural logarithms
5.4 Complex powers
5.5 Some relations to modern particle physics

6 Real-number calculus
6.1 What makes an honest function?
6.2 Slopes of functions
6.3 Higher derivatives; C1-smooth functions
6.4 The Eulerian notion of a function?
6.5 The rules of differentiation
6.6 Integration

7 Complex-number calculus
7.1 Complex smoothness; holomorphic functions
7.2 Contour integration
7.3 Power series from complex smoothness
7.4 Analytic continuation

8 Riemann surfaces and complex mappings
8.1 The idea of a Riemann surface
8.2 Conformal mappings
8.3 The Riemann sphere
8.4 The genus of a compact Riemann surface
8.5 The Riemann mapping theorem

9 Fourier decomposition and hyperfunctions
9.1 Fourier series
9.2 Functions on a circle
9.3 Frequency splitting on the Riemann sphere
9.4 The Fourier transform
9.5 Frequency splitting from the Fourier transform
9.6 What kind of function is appropriate?
9.7 Hyperfunctions

10 Surfaces
10.1 Complex dimensions and real dimensions
10.2 Smoothness, partial derivatives
10.3 Vector Fields and 1-forms
10.4 Components, scalar products
10.5 The Cauchy Riemann equations

11 Hypercomplex numbers
11.1 The algebra of quaternions
11.2 The physical role of quaternions?
11.3 Geometry of quaternions
11.4 How to compose rotations
11.5 Clifford algebras
11.6 Grassmann algebras

12 Manifolds of n dimensions
12.1 Why study higher-dimensional manifolds?
12.2 Manifolds and coordinate patches
12.3 Scalars, vectors, and covectors
12.4 Grassmann products
12.5 Integrals of forms
12.6 Exterior derivative
12.7 Volume element; summation convention
12.8 Tensors; abstract-index and diagrammatic notation
12.9 Complex manifolds

13 Symmetry groups
13.1 Groups of transformations
13.2 Subgroups and simple groups
13.3 Linear transformations and matrices
13.4 Determinants and traces
13.5 Eigenvalues and eigenvectors
13.6 Representation theory and Lie algebras
13.7 Tensor representation spaces; reducibility
13.8 Orthogonal groups
13.9 Unitary groups
13.10 Symplectic groups

14 Calculus on manifolds
14.1 Differentiation on a manifold?
14.2 Parallel transport
14.3 Covariant derivative
14.4 Curvature and torsion
14.5 Geodesics, parallelograms, and curvature
14.6 Lie derivative
14.7 What a metric can

O autorze

Roger Penrose is Emeritus Rouse Ball Professor of Mathematics at Oxford University. He has received a number of prizes and awards, including the 2020 Nobel Prize in Physics for his work on black hole formation, as well as the 1988 Wolf Prize for physics, which he shared with Stephen Hawking for their joint contribution to our understanding of the universe. His books include Cycles of Time, The Road to Reality, The Nature of Space and Time, which he wrote with Hawking, and The Emperor s New Mind. He has lectured extensively at universities throughout America. He lives in Oxford.